Abstract We construct the unitary analogue of orthogonal calculus developed by Weiss, utilising model categories to give a clear description intricacies in equivariance and homotopy theory involved. The subtle differences between real complex geometry lead calculus. To address these we spectra—a variation spectra—as for stable category. show through zig-zag Quillen equivalences that spectra wit...

We study a process calculus which combines both nondeterministic and probabilistic behavior in the style of Segala and Lynch’s probabilistic automata. We consider various strong and weak behavioral equivalences, and we provide complete axiomatizations for finite-state processes, restricted to guarded definitions in case of the weak equivalences. We conjecture that in the general case of unguard...

In this paper we prove an existence of some type of equivalences between triangulated categories of singularities for varieties of different dimensions. This class of equivalences generalizes so called Knörrer periodicity. As consequence we get equivalences between categories of D-branes of type B on Landau-Ginzburg models of different dimensions.

In the context of CCSK, a reversible extension CCS, we study observational equivalences that distinguish forward moves from backward ones. We present refinement notion forward-reverse bisimilarity and show it coincides with barbed congruence. also set sound axioms allowing one to reason equationally on process equivalences.

Greenlees defined an abelian category A whose derived category is equivalent to the rational S1-equivariant stable homotopy category whose objects represent rational S1equivariant cohomology theories. We show that in fact the model category of differential graded objects in A models the whole rational S1-equivariant stable homotopy theory. That is, we show that there is a Quillen equivalence be...